VILLEPINTE, France—Algerian boxer Imane Khelif was on the verge of a gold medal at the world championships last year when an announcement came down that would ultimately ignite the firestorm about gender and sport that has roiled the Paris Olympics.

Even though she had fought other women for years without a whisper of controversy, including at the Tokyo Games, Khelif had failed an unspecified medical test and was deemed ineligible from competition.

The timing was curious. The decision to disqualify Khelif with little explanation came down just days after she had defeated Azaliia Amineva, a previously unbeaten Russian prospect. The body that leveled the ban, the International Boxing Association, has deep financial ties to Russia and is led by a former boxer friendly with Vladimir Putin .

Now, with Khelif guaranteed a spot on the podium at the 2024 Olympics, the battle over her eligibility has exploded, sparking a global culture war that has already inflamed the U.S. presidential election. In the process, it has given Russia exactly what it wanted: a prominent place at these Games—a party to which it very pointedly wasn’t invited.

At every turn, the controversy can be traced back to Russia and tensions that have been raging for years. In the Olympic movement, it was over doping and then the invasion of Ukraine, resulting in all but a handful of Russians being excluded from these Games. There have been a host of side fights as well, including over the international governance of boxing.

Then, last week, all of those battles suddenly converged on something far more visceral: the definition of womanhood in sports.

In 2019, the International Olympic Committee took the drastic step of stripping the IBA of its authority over boxing at the Games amid accusations of widespread corruption. With that move, the IOC assumed responsibility for determining eligibility for the women’s boxing competition in Tokyo 2021—and, later, Paris—a thorny issue across all sports that is usually left up to international federations.

Now, the IOC has openly accused Russia of engineering the furor here by resurfacing the dubious situation that unfolded at the world championships run by the IBA last year—and using sports to sow discord.

“This case fits into the global narrative, which is to disrupt,” IOC spokesman Christian Klaue said Saturday, after Khelif defeated Hungary’s Luca Hámori to advance to Tuesday’s semifinal.

The IBA, in turn, is crashing an Olympics where it has no official role. Its leaders will be in Paris on Monday to hold a news conference that they say will be “dedicated to the detailed explanation of the reasons for the disqualification of two boxers.” Those boxers are Khelif and Taiwan’s Lin Yu-ting, whom the IBA also ejected from the 2023 world championships for what it said was a failed gender test. Lin, who competes in a different weight class than Khelif, won her quarterfinal bout Sunday, also guaranteeing her a medal.

IOC leaders have rejected the credibility of the IBA’s gender tests, calling the method and the process by which they were administered illegitimate. They emphasized that the boxers in question were born female and have always competed as women.

IOC President Thomas Bach has described the boxing outcry as a “politically motivated cultural war,” and it quickly entered the American political discourse. At a recent campaign event, Republican presidential nominee Donald Trump said falsely that Khelif was a successful male boxer who had “transitioned.”

The IOC has raised concerns for years about the international boxing federation and its leaders’ close ties to the Russian government. When Umar Kremlev became IBA president in late 2020, one of his first orders of business was to cut a deal with the Russian state-controlled energy supplier Gazprom to serve as a major sponsor. He also moved some of the IBA’s operations to Russia.

Kremlev, a former member of a Russian biker gang known for whipping up pro-Putin sentiment, has fiercely criticized the IOC and Bach personally. Even before the boxing controversy erupted, he called the Paris Games “an outright sodomy and the destruction of traditional values around the world.”

The IBA, like Russia’s athletes, is not involved with the Paris Games, however. That’s because in June 2022, the IOC said the IBA couldn’t organize boxing in Paris, citing “continuing and very concerning issues of the IBA, such as its governance and its refereeing and judging system.” Instead, the IOC has organized boxing at these Olympics itself.

The IOC counts boxing as an integral part of the Olympic program, given its long history and its platform for athletes from many nations, including impoverished ones. Yet the IOC’s problems with the IBA are so deep that it has given national boxing federations an ultimatum: Reach a consensus on forming a new international governing body, or boxing won’t be part of the Olympics in Los Angeles 2028.

Russian officials, who rarely miss an opportunity to blast the Paris Games, have defended Kremlev and the IBA.

“Many thanks to the IOC who organized this circus,” said Dmitry Svishchev, chairman of the State Duma Committee on Physical Culture and Sports.

Russian State Duma deputy Svetlana Zhurova told Russian website Sport-express.ru that, “If this continues to spread, it will lead to the decline of women’s sports.”

Pro-Kremlin lawmaker Alexei Pushkov , meanwhile, used the occasion to rally support for Trump.

“Trump’s supporters say he will put an end to this and ban bio-men from participating in women’s sports,” he said, according to Russia’s official parliamentary newspaper. “It would be nice to kick all the latent transgenders out of the IOC leadership.”

Tensions between Russia and the IOC have gone from bad to worse ever since the revelation of Russia’s sweeping state-sanctioned doping scheme. Russia denies its involvement, but it led to the country’s athletes being barred from competing under their flag at three consecutive Olympics—including Paris.

Write to Jared Diamond at jared.diamond@wsj.com